I
nte
rna
t
io
na
l J
o
urna
l o
f
E
lect
rica
l a
nd
Co
m
p
ute
r
E
ng
in
ee
ring
(
I
J
E
CE
)
Vo
l.
7
,
No
.
1
,
Feb
r
u
ar
y
201
7
,
p
p
.
5
2
1
~
5
2
5
I
SS
N:
2088
-
8708
,
DOI
: 1
0
.
1
1
5
9
1
/
i
j
ec
e
.
v
7
i
1
.
pp
521
-
5
2
5
521
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3
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C
y
c
li
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Re
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Co
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s
(CRCs
)
a
re
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p
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f
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m
a
in
tain
in
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teg
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a
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CRC
p
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a
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a
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l
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ff
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ted
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e
p
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ly
n
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c
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d
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ta
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g
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w
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m
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M
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CRC
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p
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,
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Clas
sic
a
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a
p
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to
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K
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C
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In
stit
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te o
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C
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p
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A
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r
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Ah
m
ed
Salih
Kh
ir
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R
esear
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ter
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s
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8
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m
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1.
I
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D
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C
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cl
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R
ed
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d
an
c
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C
h
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k
(
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co
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ata
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ig
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m
m
u
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s
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d
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s
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h
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y
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t
a
s
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e
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f
d
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t
w
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n
o
d
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i
n
a
c
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m
m
u
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lin
k
[
1
]
.
Var
io
u
s
C
R
C
i
m
p
le
m
e
n
tatio
n
s
ex
is
t
in
d
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f
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er
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t
ap
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s
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f
r
o
m
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m
b
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d
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n
et
w
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r
k
ap
p
licatio
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s
[
1
]
to
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ele
s
s
n
et
w
o
r
k
s
[
2
]
,
to
co
m
m
u
n
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n
p
r
o
to
co
ls
s
u
ch
as
USB
3
[
3
]
.
T
h
eir
w
id
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e
to
th
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i
m
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lic
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o
o
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en
co
d
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g
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n
d
d
ec
o
d
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p
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m
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,
an
d
g
o
o
d
lev
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s
o
f
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r
o
r
d
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tio
n
[
4
]
.
A
s
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ata
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r
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g
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cr
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s
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tan
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m
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le
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as
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[
5
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m
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s
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b
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[
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w
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
J
E
C
E
Vo
l.
7
,
No
.
1
,
Feb
r
u
ar
y
201
7
:
5
2
1
–
525
522
"g
o
o
d
"
g
en
er
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p
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p
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s
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1
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.
A
co
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f
o
r
m
a
n
ce
o
f
er
r
o
r
d
etec
tio
n
an
d
h
o
w
h
ig
h
er
le
v
el
s
o
f
o
p
ti
m
izatio
n
m
a
y
b
e
ac
h
iev
ed
b
y
u
s
in
g
n
e
w
er
p
u
b
lis
h
ed
C
R
C
p
o
l
y
n
o
m
i
als.
T
h
e
p
ap
er
th
e
n
p
r
o
v
id
es
an
ex
h
au
s
ti
v
e
s
u
r
v
e
y
o
f
C
R
C
p
o
l
y
n
o
m
ials
f
r
o
m
3
-
to
1
5
-
b
it
alo
n
g
w
ith
a
d
is
cu
s
s
io
n
o
f
1
6
-
b
it
p
o
ly
n
o
m
ia
ls
.
T
h
e
p
ap
er
also
d
ef
in
e
s
"
g
o
o
d
"
p
o
ly
n
o
m
ia
l
s
as
th
o
s
e
ac
h
ie
v
i
n
g
t
h
e
m
ax
i
m
u
m
Ha
m
m
i
n
g
Dis
ta
n
ce
f
o
r
th
e
lo
n
g
est
d
ata
w
o
r
d
alo
n
g
w
it
h
o
th
er
co
n
s
id
er
atio
n
s
.
Desp
ite
th
e
co
m
p
r
e
h
en
s
i
v
e
n
at
u
r
e
o
f
th
is
r
esear
ch
,
C
R
C
co
d
es
b
e
y
o
n
d
1
6
p
ar
ity
b
its
w
er
e
av
o
id
ed
d
u
e
to
t
h
e
lar
g
e
n
u
m
b
er
o
f
p
o
s
s
ib
ilit
ies
th
a
t
h
ad
to
b
e
in
v
est
ig
ated
.
Ho
w
ev
er
,
ce
r
tain
clas
s
es
o
f
2
4
-
an
d
3
2
-
b
it
C
R
C
co
d
es
w
er
e
in
v
es
tig
a
ted
b
y
[
7
]
,
w
h
er
ea
s
a
co
m
p
r
e
h
en
s
iv
e
s
ea
r
ch
f
o
r
C
R
C
co
d
es
w
i
th
3
2
p
ar
it
y
b
its
w
a
s
u
n
d
er
tak
en
b
y
[
8
]
.
Si
m
i
lar
to
[
1
]
,
an
an
al
y
s
is
o
f
C
R
C
co
d
e
s
tan
d
ar
d
s
,
n
a
m
el
y
,
C
R
C
-
1
2
,
A
NSI
a
n
d
C
C
I
7
T
X.
2
5
,
p
r
o
v
ed
th
at
th
e
s
ta
n
d
ar
d
s
w
er
e
n
o
t
o
n
p
ar
w
ith
t
h
e
b
est
p
o
s
s
ib
le
C
R
C
i
m
p
le
m
en
ta
tio
n
s
a
n
d
t
h
at
t
h
e
s
it
u
atio
n
s
ee
m
ed
u
n
l
ik
el
y
to
ch
a
n
g
e
d
u
e
to
ec
o
n
o
m
ic
co
n
ce
r
n
s
[
4
]
.
T
h
is
co
u
p
led
w
it
h
t
h
e
u
s
e
o
f
C
R
C
s
in
h
i
g
h
-
t
h
r
o
u
g
h
p
u
t
ap
p
licatio
n
s
s
u
ch
a
s
USB
3
[
3
]
,
h
as
m
ad
e
p
ar
allel
C
R
C
cir
c
u
itr
y
d
esi
g
n
,
an
i
m
p
o
r
tan
t a
r
ea
o
f
r
esear
ch
[
9
]
.
P
er
f
o
r
m
a
n
ce
o
f
C
R
C
i
m
p
le
m
en
tatio
n
s
cr
ea
ted
b
y
p
o
l
y
n
o
m
ials
w
it
h
a
d
eg
r
ee
o
f
1
6
an
d
ab
o
v
e
f
o
r
er
r
o
r
d
etec
tio
n
in
co
m
m
u
n
ic
atio
n
s
y
s
te
m
s
w
as
e
v
al
u
ated
b
y
[
4
]
.
T
h
e
p
r
o
p
er
ties
o
f
m
i
n
i
m
u
m
d
is
tan
ce
,
"
p
r
o
p
er
n
ess
"
an
d
u
n
d
etec
ted
er
r
o
r
p
r
o
b
a
b
ilit
y
f
o
r
b
in
ar
y
s
y
m
m
etr
ic
ch
a
n
n
els
(
B
SC
)
ar
e
ca
lcu
lated
a
n
d
co
m
p
ar
ed
w
it
h
ex
i
s
ti
n
g
s
tan
d
a
r
d
s
.
T
h
e
co
r
e
o
f
C
R
C
i
m
p
le
m
en
ta
tio
n
s
d
ep
en
d
s
o
n
th
e
p
o
l
y
n
o
m
ial
ch
o
s
en
.
Desp
ite
t
h
eir
i
m
p
o
r
tan
ce
in
en
s
u
r
in
g
d
ata
in
te
g
r
it
y
,
a
co
m
p
r
eh
en
s
i
v
e
r
esear
ch
d
is
c
lo
s
ed
th
at
m
o
s
t
p
u
b
lis
h
ed
C
R
C
p
o
l
y
n
o
m
ial
s
ar
e
eith
er
o
p
tim
a
l
w
h
en
l
i
m
ited
to
ce
r
tain
m
ess
a
g
e
le
n
g
th
s
o
r
in
f
er
io
r
t
o
alter
n
ativ
e
s
.
T
h
e
latter
is
s
u
p
p
o
r
ted
b
y
t
h
e
f
ac
t
th
at
m
a
n
y
ap
p
licatio
n
s
u
ti
lize
C
R
C
s
th
at
o
f
f
er
m
u
c
h
le
s
s
er
r
o
r
d
etec
tio
n
ca
p
ab
ilit
y
t
h
a
n
p
o
s
s
ib
le
f
o
r
a
ce
r
tain
C
R
C
b
it
v
al
u
e.
T
h
is
m
a
y
also
b
e
s
u
p
p
o
r
ted
b
y
th
e
lack
o
f
"
to
o
ls
an
d
d
ata
tab
les"
f
o
r
m
ea
s
u
r
i
n
g
p
o
l
y
n
o
m
ial
p
er
f
o
r
m
a
n
ce
[
1
]
.
W
ith
r
eg
ar
d
s
to
p
o
l
y
n
o
m
ial
s
elec
tio
n
,
t
h
e
c
u
r
r
en
t
la
n
d
s
ca
p
e
s
u
f
f
er
s
f
r
o
m
th
r
ee
i
s
s
u
es
:
(
1
)
lacu
n
ae
ex
is
t
i
n
t
h
e
cu
r
r
en
t
p
u
b
li
s
h
e
d
p
o
ly
n
o
m
ials
s
et
(
2
)
n
o
s
p
ec
if
ic
g
u
id
an
ce
ex
is
t
s
o
n
t
h
e
v
iab
ilit
y
o
f
ce
r
tai
n
p
o
ly
n
o
m
ia
ls
in
ce
r
tai
n
co
n
tex
t
s
,
an
d
(
3
)
lacu
n
ae
w
it
h
r
esp
ec
t
to
p
u
b
lis
h
ed
q
u
an
titati
v
e
an
al
y
s
e
s
[
1
]
.
R
esear
ch
h
as
s
h
o
w
n
th
a
t
v
ar
y
in
g
p
o
l
y
n
o
m
ial
s
w
it
h
i
n
a
ce
r
tain
s
ize
as
w
e
ll
as
v
ar
y
i
n
g
th
e
s
ize,
p
r
o
d
u
ce
s
d
if
f
er
en
t
r
esu
lt
s
w
it
h
r
es
p
ec
t to
er
r
o
r
d
e
tectin
g
p
er
f
o
r
m
a
n
ce
[
4
]
.
2.
M
E
T
H
O
D
O
L
O
G
Y
W
ith
r
eg
ar
d
s
to
e
m
b
ed
d
ed
n
et
w
o
r
k
s
,
an
attr
ib
u
te
o
f
co
n
ce
r
n
w
it
h
C
R
C
i
m
p
le
m
e
n
ta
tio
n
is
t
h
e
Ha
m
m
i
n
g
D
is
ta
n
ce
(
HD)
[
1
]
.
HD
is
th
e
lea
s
t
b
it
in
v
er
s
io
n
s
t
h
at
h
a
v
e
to
b
e
in
te
g
r
ated
in
to
a
m
es
s
a
g
e
to
g
en
er
ate
a
n
er
r
o
r
th
at
i
s
"
u
n
d
etec
tab
le
b
y
t
h
at
m
ess
a
g
e
'
s
C
R
C
-
b
ased
Fra
m
e
C
h
e
ck
Seq
u
e
n
ce
"
.
T
h
e
p
r
o
b
a
b
ilit
y
o
f
s
u
c
h
a
d
ata
co
r
r
u
p
tio
n
o
cc
u
r
r
in
g
i
s
s
m
all
b
u
t
n
o
n
et
h
eles
s
,
th
e
lea
s
t
n
u
m
b
er
o
f
b
it
in
v
er
s
io
n
s
i
n
o
r
d
er
to
ac
h
iev
e
th
e
a
f
o
r
e
m
e
n
tio
n
ed
u
n
d
etec
tab
le
er
r
o
r
s
i
s
c
r
u
cial
i
n
C
R
C
p
o
l
y
n
o
m
ial
d
es
ig
n
[
1
]
;
s
ize
o
f
b
its
an
d
d
ata
w
o
r
d
s
ar
e
also
to
b
e
co
n
s
id
er
ed
s
in
ce
t
h
e
y
a
f
f
ec
t e
r
r
o
r
-
d
etec
tio
n
p
er
f
o
r
m
an
ce
[
4
]
.
C
o
n
n
ec
ted
w
it
h
HD
is
th
e
at
t
r
ib
u
te,
Ha
m
m
i
n
g
W
eig
h
t
(
H
W
)
.
Fo
r
a
HW
o
f
N,
N
is
t
h
e
n
u
m
b
er
o
f
u
n
d
etec
ted
er
r
o
r
p
r
o
b
a
b
ilit
ies
b
y
a
C
R
C
i
m
p
le
m
en
tatio
n
w
i
th
r
esp
ec
t
to
a
s
p
ec
i
f
ic
p
o
l
y
n
o
m
ial.
A
co
llectio
n
o
f
HW
s
ca
p
t
u
r
es
p
er
f
o
r
m
a
n
ce
f
o
r
d
i
f
f
er
e
n
t
n
u
m
b
er
s
o
f
b
it
s
co
r
r
u
p
ted
in
a
m
e
s
s
a
g
e
at
a
p
ar
ticu
lar
d
ata
w
o
r
d
len
g
th
.
T
h
e
f
ir
s
t n
o
n
-
ze
r
o
Ha
m
m
in
g
w
ei
g
h
t d
eter
m
i
n
es a
c
o
d
e’
s
HD.
T
h
e
g
o
al
o
f
f
i
n
d
in
g
a
g
o
o
d
C
R
C
p
o
l
y
n
o
m
ial
is
to
e
n
s
u
r
e
o
p
ti
m
izatio
n
,
i.e
.
,
to
m
ax
i
m
ize
th
e
HD
a
n
d
m
i
n
i
m
ize
th
e
HW
.
T
h
e
class
ical
w
a
y
to
f
i
n
d
s
u
c
h
p
o
l
y
n
o
m
i
als
is
to
tr
y
all
p
o
s
s
ib
le
ca
s
es
o
f
p
o
ly
n
o
m
ia
ls
an
d
d
ata
b
it
er
r
o
r
s
(
1
-
,
2
-
,
3
-
,
m
es
s
ag
e
len
g
t
h
er
r
o
r
s
)
,
an
d
th
en
s
elec
t
th
e
o
p
ti
m
al
o
n
e.
T
h
is
m
e
th
o
d
is
s
u
itab
le
f
o
r
s
m
al
l
v
alu
e
s
o
f
d
ata
w
o
r
d
l
en
g
t
h
s
a
n
d
p
o
l
y
n
o
m
ial
d
eg
r
ee
.
Ho
w
e
v
er
,
f
o
r
lar
g
er
v
al
u
es,
co
m
p
u
tat
io
n
al
co
m
p
le
x
it
y
i
n
cr
ea
s
es a
n
d
th
u
s
m
ak
e
s
s
o
l
u
tio
n
s
i
m
p
o
s
s
ib
le
o
n
to
d
ay
'
s
co
m
p
u
ter
s
.
W
e
p
r
o
p
o
s
e
s
o
lv
in
g
t
h
e
is
s
u
e
o
f
r
ed
u
cin
g
co
m
p
u
tatio
n
al
co
m
p
lex
i
t
y
b
y
u
s
i
n
g
t
h
e
co
n
ce
p
t
o
f
Gen
etic
A
l
g
o
r
ith
m
s
(
G
A
)
,
th
u
s
tr
ea
ti
n
g
t
h
e
p
r
o
b
le
m
as
an
o
p
ti
m
izatio
n
p
r
o
b
lem
.
G
A
i
s
a
t
y
p
e
o
f
ev
o
lu
tio
n
ar
y
co
m
p
u
tatio
n
m
et
h
o
d
,
b
u
t
h
a
s
n
o
ag
r
ee
d
u
p
o
n
d
ef
i
n
itio
n
w
h
ich
d
i
f
f
er
en
tiate
s
it
f
r
o
m
o
th
er
ev
o
l
u
tio
n
-
co
m
p
u
tatio
n
m
et
h
o
d
s
.
Ho
w
e
v
er
,
t
h
er
e
ar
e
s
o
m
e
f
ea
t
u
r
es
w
h
i
c
h
co
n
s
is
te
n
tl
y
p
r
ese
n
t
th
e
m
s
el
v
es
i
n
G
A
m
et
h
o
d
s
:
“
p
o
p
u
latio
n
s
o
f
ch
r
o
m
o
s
o
m
e
s
,
s
elec
tio
n
ac
co
r
d
in
g
to
f
itn
e
s
s
,
cr
o
s
s
o
v
er
to
p
r
o
d
u
ce
n
e
w
o
f
f
s
p
r
i
n
g
,
an
d
r
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Fit
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p
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1
4
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d
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t
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m
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also
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t
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b
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k
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to
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f
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m
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t
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s
y
m
m
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ith
m
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m
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m
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t
ca
n
en
cr
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p
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d
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t
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n
1
2
8
-
b
it
b
lo
c
k
s
b
y
u
s
in
g
1
2
8
,
1
9
2
,
an
d
2
5
6
-
b
it
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to
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ap
h
ic
k
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s
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e
w
il
l b
e
u
s
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g
a
1
2
8
-
b
it c
r
y
p
to
g
r
ap
h
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k
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f
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r
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p
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licatio
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.
3.
RE
SU
L
T
S
A
ND
D
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SS
CUSS
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e
M
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B
en
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n
m
en
t
w
it
h
its
b
u
ilt
-
i
n
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A
to
o
lb
o
x
.
T
h
e
f
ir
s
t
e
x
p
er
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m
e
n
t
co
n
s
is
ted
o
f
d
ata
p
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k
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f
4
8
b
its
,
an
d
w
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th
e
h
ig
h
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t
d
eg
r
ee
o
f
th
e
g
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ato
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p
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ly
n
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m
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w
as
1
6
.
B
i
t
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r
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r
ca
s
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r
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g
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f
r
o
m
1
to
6f
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f
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1
0
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0
0
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co
m
b
i
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s
w
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test
ed
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T
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HD
w
a
s
ch
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to
b
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6
.
T
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a
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ch
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s
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f
o
r
th
is
ex
p
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m
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w
as
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h
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p
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n
o
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l
f
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n
d
b
y
[
4
]
,
w
it
h
a
h
ex
v
al
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e
o
f
0
x
C
8
6
C
.
A
n
a
n
al
y
s
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s
b
y
[
1
]
f
o
u
n
d
it
to
th
e
b
est
a
m
o
n
g
s
t
m
an
y
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th
er
s
f
o
r
a
d
ata
w
o
r
d
s
ize
o
f
4
8
b
its
.
R
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lt
s
ar
e
s
h
o
w
n
in
T
ab
le
1
.
T
ab
le
1
.
R
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lta
n
t P
o
ly
n
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m
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Vs
[
4
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,
T
ested
W
ith
1
0
,
0
0
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C
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m
b
i
n
atio
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s
HD
P
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2
6
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[
4
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0
x
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6
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6
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2
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2
1
9
1
A
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h
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t
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t
p
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y
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m
ial
h
a
s
a
lo
w
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HD
th
a
n
[
4
]
,
th
e
s
u
m
o
f
u
n
d
etec
ted
er
r
o
r
s
in
5
-
b
i
t
an
d
6
-
b
it
ca
s
e
s
is
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er
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h
an
u
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r
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r
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in
[
4
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f
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r
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its
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o
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p
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h
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.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
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2
0
8
8
-
8708
I
J
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C
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Vo
l.
7
,
No
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1
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Feb
r
u
ar
y
201
7
:
5
2
1
–
525
524
T
ab
le
2
.
R
esu
lta
n
t P
o
ly
n
o
m
ial
Vs
[
4
]
,
T
ested
W
ith
3
0
0
,
0
0
0
C
o
m
b
i
n
atio
n
s
HD
P
o
l
y
n
o
mi
a
l
1
b
i
t
2
b
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t
s
3
b
i
t
s
4
b
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t
s
5
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2
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4
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0
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8
6
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6
0
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1
2
1
9
1
I
t
is
clea
r
th
at
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e
w
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ial
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p
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u
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e
,
an
d
th
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s
[
4
]
'
s
a
s
w
ell.
T
h
e
n
u
m
b
er
o
f
u
n
d
etec
ted
er
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o
r
p
r
o
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ab
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h
as
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r
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ed
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ig
n
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ican
tl
y
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o
m
th
e
p
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u
s
ex
p
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m
en
t,
r
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u
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g
in
5
7
co
m
p
ar
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w
it
h
1
8
3
f
r
o
m
th
e
p
r
ev
io
u
s
e
x
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er
i
m
e
n
t,
f
o
r
5
-
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its
.
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h
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i
m
p
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v
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m
en
t i
n
6
-
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it
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t
w
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ize
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6
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d
4
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0
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at
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is
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w
it
h
a
m
in
i
m
u
m
v
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o
f
6
.
T
ab
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3
s
h
o
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s
th
e
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lta
n
t
p
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n
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m
ial,
th
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n
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m
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s
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m
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s
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e
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cr
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alo
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g
w
it
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ize,
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6
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n
r
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d
o
m
l
y
ch
o
s
e
n
an
d
test
ed
.
T
h
e
d
ata
w
o
r
d
s
ize
w
a
s
1
1
2
b
it.
T
h
e
b
en
ef
it
o
f
ad
d
in
g
en
cr
y
p
tio
n
as
w
e
ll
as
a
h
ea
d
er
ca
n
b
e
clea
r
ly
s
ee
n
.
T
h
e
n
u
m
b
er
o
f
u
n
d
etec
ted
er
r
o
r
p
r
o
b
ab
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ies
w
it
h
o
u
t
en
cr
y
p
tio
n
a
n
d
a
h
ea
d
er
w
as
1
4
1
.
A
d
d
i
n
g
e
n
cr
y
p
ti
o
n
r
ed
u
ce
d
it
to
6
0
an
d
ad
d
in
g
a
h
ea
d
er
alo
n
g
w
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th
en
cr
y
p
tio
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d
ec
r
ea
s
ed
it
ev
en
f
u
r
th
er
,
en
ab
li
n
g
t
h
e
C
R
C
i
m
p
le
m
e
n
tatio
n
to
ca
tch
all
p
o
s
s
ib
le
er
r
o
r
s
.
T
ab
le
3
.
No
.
Of
Un
d
etec
ted
E
r
r
o
r
P
r
o
b
ab
ilit
ies f
o
r
t
h
e
P
o
ly
n
o
m
ial
0
x
8
9
4
8
P
o
l
y
n
o
mi
a
l
C
R
C
C
R
C
a
n
d
E
n
c
r
y
p
t
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n
C
R
C
a
n
d
E
n
c
r
y
p
t
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o
n
w
i
t
h
H
e
a
d
e
r
0
x
8
9
4
8
1
4
1
60
0
4.
CO
NCLU
SI
O
N
AND
F
U
T
U
RE
WO
RK
Ou
r
w
o
r
k
s
h
o
w
ed
h
o
w
u
s
in
g
a
GA
ap
p
r
o
ac
h
d
ec
r
ea
s
ed
th
e
n
u
m
b
er
o
f
p
o
s
s
ib
le
s
o
lu
t
io
n
ca
n
d
id
ates
f
o
r
f
i
n
d
in
g
a
n
o
p
ti
m
al
p
o
l
y
n
o
m
ial
f
o
r
u
s
e
in
a
C
R
C
i
m
p
le
m
en
tatio
n
.
W
e
co
m
p
ar
ed
th
e
r
e
s
u
lta
n
t
p
o
l
y
n
o
m
ials
ag
ain
s
t
a
b
en
c
h
m
ar
k
[
4
]
f
o
r
a
d
ata
w
o
r
d
le
n
g
t
h
o
f
4
8
b
its
.
W
e
also
ev
al
u
ated
t
h
e
e
f
f
ec
t
o
f
e
n
cr
y
p
tio
n
o
n
d
ata
h
ea
d
er
s
in
a
C
R
C
i
m
p
le
m
en
tatio
n
;
w
e
f
o
u
n
d
th
at
en
cr
y
p
tio
n
i
m
p
r
o
v
es
p
er
f
o
r
m
a
n
ce
o
f
a
C
R
C
i
m
p
le
m
en
ta
tio
n
.
Ou
r
ev
al
u
atio
n
,
h
o
w
ev
er
,
is
n
o
t
co
m
p
r
eh
en
s
i
v
e
w
h
ic
h
l
ea
v
es
r
o
o
m
f
o
r
f
u
t
u
r
e
w
o
r
k
.
A
m
o
r
e
th
o
r
o
u
g
h
e
v
al
u
atio
n
o
f
u
s
i
n
g
GA
f
o
r
d
i
f
f
er
e
n
t
d
ata
w
o
r
d
le
n
g
t
h
s
a
n
d
C
R
C
b
it
len
g
t
h
w
o
u
ld
ad
d
s
tr
en
g
t
h
to
th
e
p
r
o
p
o
s
al
at
h
a
n
d
.
Si
m
i
lar
ly
,
a
t
h
o
r
o
u
g
h
b
e
n
ch
m
ar
k
an
a
l
y
s
i
s
o
f
r
es
u
lta
n
t
p
o
l
y
n
o
m
ials
u
s
in
g
G
A
f
o
r
th
e
v
ar
io
u
s
d
ata
w
o
r
d
le
n
g
th
s
a
n
d
C
R
C
b
it le
n
g
th
w
o
u
ld
p
r
o
v
e
t
h
e
v
alid
it
y
o
f
o
u
r
m
e
th
o
d
ac
r
o
s
s
a
w
id
er
s
co
p
e
o
f
C
R
C
i
m
p
le
m
e
n
tatio
n
s
.
ACK
NO
WL
E
D
G
E
M
E
NT
S
T
h
e
r
esear
ch
er
s
w
is
h
to
t
h
an
k
Un
i
v
er
s
iti
Keb
an
g
s
aa
n
Ma
la
y
s
ia
(
UK
M)
f
o
r
s
u
p
p
o
r
tin
g
t
h
is
w
o
r
k
b
y
r
esear
ch
g
r
an
ts
: D
a
n
a
I
m
p
a
k
P
er
d
an
a
(
DI
P
-
2
0
1
4
-
0
3
7
)
.
RE
F
E
R
E
NC
E
S
[1
]
P
.
Ko
o
p
m
a
n
a
n
d
T
.
Ch
a
k
ra
v
a
rty
,
“
C
y
c
li
c
Re
d
u
n
d
a
n
c
y
Co
d
e
(CRC)
P
o
ly
n
o
m
ial
S
e
l
e
c
ti
o
n
F
o
r
Em
b
e
d
d
e
d
Ne
tw
o
rk
s”
,
In
t.
Co
n
f.
De
p
e
n
d
a
b
l
e
S
y
st.
Ne
two
rk
s
,
2
0
0
4
,
p
p
.
1
–
1
1
,
2
0
0
4
.
[2
]
V
.
Ch
e
a
,
M
.
V.
M
a
rti
n
,
a
n
d
R.
L
i
sc
a
n
o
,
“
Ha
m
m
in
g
d
istan
c
e
a
s
a
m
e
tri
c
f
o
r
th
e
d
e
tec
ti
o
n
o
f
c
rc
-
b
a
se
d
sid
e
-
c
h
a
n
n
e
l
c
o
m
m
u
n
ica
ti
o
n
s
in
8
0
2
.
1
1
w
irele
ss
n
e
tw
o
rk
s”
,
in
IEE
E
c
o
n
fer
e
n
c
e
o
n
c
o
mm
u
n
ica
ti
o
n
s
a
n
d
n
e
two
rk
s
e
c
u
rity
(
c
n
s)
,
2
0
1
5
,
p
p
.
2
1
8
–
2
2
6
.
[3
]
Y.
W
u
a
n
d
Y.
Qiu
,
“
T
h
e
8
-
b
it
p
a
ra
ll
e
l
c
rc
-
3
2
re
se
a
r
c
h
a
n
d
im
p
le
m
e
n
tatio
n
i
n
u
sb
3
.
0
”
,
in
I
n
ter
n
a
t
io
n
a
l
c
o
n
fer
e
n
c
e
o
n
C
o
mp
u
ter
sc
ien
c
e
se
rv
ice
s
y
st
e
m (
c
ss
s)
,
2
0
1
2
,
p
p
.
1
0
7
9
–
1
0
8
2
.
[4
]
T
.
Ba
ich
e
v
a
,
S
.
Do
d
u
n
e
k
o
v
,
a
n
d
P
.
Ka
z
a
k
o
v
,
“
Un
d
e
tec
ted
e
rro
r
p
ro
b
a
b
il
it
y
p
e
rf
o
r
m
a
n
c
e
o
f
c
y
c
li
c
re
d
u
n
d
a
n
c
y
-
c
h
e
c
k
c
o
d
e
s o
f
1
6
-
b
it
re
d
u
n
d
a
n
c
y
”
,
in
IE
E
Pro
c
e
e
d
i
n
g
s
-
C
o
mm
u
n
i
c
a
ti
o
n
s
,
v
o
l.
1
4
7
,
n
o
.
5
,
p
p
.
2
5
3
–
2
5
6
.
[5
]
F
.
M
o
n
teiro
,
A
.
Da
n
d
a
c
h
e
,
A
.
M
’S
ir,
a
n
d
B.
L
e
p
ley
,
“
A
p
o
l
y
n
o
m
ial
d
iv
isio
n
p
i
p
e
li
n
e
d
a
rc
h
it
e
c
tu
re
f
o
r
c
rc
e
rro
r
d
e
tec
ti
n
g
c
o
d
e
s”
,
in
T
h
e
1
3
th
i
n
te
rn
a
ti
o
n
a
l
c
o
n
fer
e
n
c
e
o
n
M
icr
o
e
lec
tro
n
ics
,
2
0
0
1
,
v
o
l
.
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